Will a TV this old work with a converter box?

Aside from that, there could be an AC shock hazard if the TV is transformerless (even if the TV has a transformer power supply, the box may not; transformer-powered and transformerless equipment do not mix), and aside from
that, if this set has anything other than a 41-MHz IF strip it probably won't work with an ATSC->NTSC box, since these are designed to be used with modern sets -- "modern" in this context meaning TVs with 41-MHz IFs. I don't see how these boxes would work with a late '40s set such as this.